{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YCZ45RU7FBM6RCI7RIYZ6GE63H","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0e95bcf5313e60819151dcb19dc9365d58444b5a39290703f6b026af9aaeeb8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-10T16:27:43Z","title_canon_sha256":"5ffe01b2a8a080cf8a5472b0f29e385785e366204a1782bd59f86d63ce4d002e"},"schema_version":"1.0","source":{"id":"1309.2569","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2569","created_at":"2026-05-18T03:13:44Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2569v1","created_at":"2026-05-18T03:13:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2569","created_at":"2026-05-18T03:13:44Z"},{"alias_kind":"pith_short_12","alias_value":"YCZ45RU7FBM6","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YCZ45RU7FBM6RCI7","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YCZ45RU7","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:3f59a282a9a79fb97862ddf483adae9b755805115363c06c3a22687df834b45b","target":"graph","created_at":"2026-05-18T03:13:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study asymptotic behavior of the dimensions of the homology groups of subgroups of finite index in finitely generated subgroups of pro-$p$ extension of centralizers of free pro-$p$ groups. We also prove group theoretic structure properties of such pro-$p$ groups that are of independent interest.","authors_text":"Dessislava Kochloukova, Pavel Zalesskii","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-10T16:27:43Z","title":"Subgroups and Homology of Extensions of Centralizers of Pro-p Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2569","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b89bb67eff238ef26f99d24af014c714e0cbb3f9b8372f4128cb2561635beafb","target":"record","created_at":"2026-05-18T03:13:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0e95bcf5313e60819151dcb19dc9365d58444b5a39290703f6b026af9aaeeb8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-10T16:27:43Z","title_canon_sha256":"5ffe01b2a8a080cf8a5472b0f29e385785e366204a1782bd59f86d63ce4d002e"},"schema_version":"1.0","source":{"id":"1309.2569","kind":"arxiv","version":1}},"canonical_sha256":"c0b3cec69f2859e8891f8a319f189ed9f529a381367487b80aa36db8f1b27537","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0b3cec69f2859e8891f8a319f189ed9f529a381367487b80aa36db8f1b27537","first_computed_at":"2026-05-18T03:13:44.201582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:44.201582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iqC8T4JNUPvcq1d7+PnEt3oyvSqB3jxql4PYKv3iZpPn56Rh/BVU2tRO0MInJG3Ii1ZxRp0XOQxmkXjEurxABQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:44.202496Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.2569","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b89bb67eff238ef26f99d24af014c714e0cbb3f9b8372f4128cb2561635beafb","sha256:3f59a282a9a79fb97862ddf483adae9b755805115363c06c3a22687df834b45b"],"state_sha256":"c8e1ceea01d13064b1b5ceea30ac02469e4656aed86ffeaacc1a2f7c731d49ec"}